I usually wash the fleece whole. Just part fill the bath and add a little soap (I use ecover for wool) and just move the fleece a little to dislodge and submerge it. If your fleece is cleanish you haven't really got to clean it - just get rid of the skirt that is muddy or caked. It really depends what you want to do with it. If it's for spinning, you don't really need to clean it, especially if it's your own and you know it's not been dipped or anything. If it's for felting, you clean it, and you can afford to clean it a bit more because you don't really need the lanolin like you would for spinning.
Some people use washing up liquid, which is far too sudsy - they end up stripping the lanolin for spinning, and have to spray it with some oil (which I think is quite mad). When most of the dirt is gone, just empty the bath, refill it and rinse, and then when you empty it the next time, I tend to give it a once over with a shower attachment. Don't wring the fleece, just squeeze out as much water as you can and dry it on an airer somewhere ( I tend to dry it outside when I've got nice weather).